ABSTRACT
This chapter describes fundamentals of solution schemes for computing the entire fluid flow field and discusses the typical schemes for solving fluid flow problems. The marker-and-cell, simplified marker-and-cell and solution algorithm- volume of fluid methods were developed for solving the fluid flow problems. The application of the explicit scheme might be limited for the simulation of fluid flow in a mushy state due to the complicating phenomena, such as non-Newtonian behavior, double diffusive convection, and damping effect. The SIMPLE algorithm is an implicit scheme treating the pressure gradient through combining the momentum and continuity equations, and is well known as one of the most accurate algorithms for solving fluid flow problems including two-phase flows. However, the SIMPLE method has a significant limitation. It takes a large computational time to solve simultaneous equations iteratively when we simulate transient fluid flow problems, such as mould filling with free surfaces.
